Mesh parameterization for an open connected surface without partition

A novel mesh parametrization method for an open connected surface is presented. The parametrization method is based on Hessian-based locally linear embedding (HLLE). Our method operates directly on the surface without using any partition technique and can preserve the local and global structure, while partition-based methods often produce high distortion and discontinuity nearby partition boundaries. In addition, some examples about texture mapping show the efficiency of our method.

[1]  Ron Kimmel,et al.  Texture Mapping Using Surface Flattening via Multidimensional Scaling , 2002, IEEE Trans. Vis. Comput. Graph..

[2]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..

[3]  Pedro V. Sander,et al.  Texture mapping progressive meshes , 2001, SIGGRAPH.

[4]  D. Donoho,et al.  Hessian Eigenmaps : new locally linear embedding techniques for high-dimensional data , 2003 .

[5]  D. Donoho,et al.  Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Kai Hormann,et al.  Surface Parameterization: a Tutorial and Survey , 2005, Advances in Multiresolution for Geometric Modelling.

[7]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[8]  Peter Liepa,et al.  Filling Holes in Meshes , 2003, Symposium on Geometry Processing.

[9]  Xianfeng Gu,et al.  Parametrization for surfaces with arbitrary topologies , 2003 .

[10]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[11]  Mark Meyer,et al.  Intrinsic Parameterizations of Surface Meshes , 2002, Comput. Graph. Forum.

[12]  Bruno Lévy,et al.  Least squares conformal maps for automatic texture atlas generation , 2002, ACM Trans. Graph..

[13]  Tao Ju,et al.  Robust repair of polygonal models , 2004, ACM Trans. Graph..

[14]  Kun Zhou,et al.  Iso-charts: stretch-driven mesh parameterization using spectral analysis , 2004, SGP '04.

[15]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.